Performance improvement of professional printing systems : from theory to practice Ezzeldin Mahdy Abdelmonem, M.

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1 Performance improvement of professional printing systems : from theory to practice Ezzeldin Mahdy Abdelmonem, M. DOI: /IR Published: 01/01/2012 Document Version Publisher s PDF, also known as Version of Record (includes final page, issue and volume numbers) Please check the document version of this publication: A submitted manuscript is the author's version of the article upon submission and before peer-review. There can be important differences between the submitted version and the official published version of record. People interested in the research are advised to contact the author for the final version of the publication, or visit the DOI to the publisher's website. The final author version and the galley proof are versions of the publication after peer review. The final published version features the final layout of the paper including the volume, issue and page numbers. Link to publication Citation for published version (APA): Ezzeldin Mahdy Abdelmonem, M. (2012). Performance improvement of professional printing systems : from theory to practice Eindhoven: Technische Universiteit Eindhoven DOI: /IR General rights Copyright and moral rights for the publications made accessible in the public portal are retained by the authors and/or other copyright owners and it is a condition of accessing publications that users recognise and abide by the legal requirements associated with these rights. Users may download and print one copy of any publication from the public portal for the purpose of private study or research. You may not further distribute the material or use it for any profit-making activity or commercial gain You may freely distribute the URL identifying the publication in the public portal? Take down policy If you believe that this document breaches copyright please contact us providing details, and we will remove access to the work immediately and investigate your claim. Download date: 20. Jun. 2018

2 Performance Improvement of Professional Printing Systems: from theory to practice PROEFSCHRIFT ter verkrijging van de graad van doctor aan de Technische Universiteit Eindhoven, op gezag van de Rector Magnificus, prof.dr.ir. C.J. van Duijn, voor een commissie aangewezen door het College voor Promoties in het openbaar te verdedigen op woensdag 25 april 2012 om uur door Mohamed Ezzeldin Mahdy Abdelmonem geboren te Menia, Egypte

3 Dit proefschrift is goedgekeurd door de promotoren: prof.dr.ir. P.P.J. van den Bosch en prof.dr. S. Weiland This work has been carried out as part of the OCTOPUS project with Océ Technologies B.V. This project is under the responsibility of the Embedded Systems Institute. This dissertation has been completed in fulfillment of the requirements of the Dutch Institute of Systems and Control DISC. A catalogue record is available from the Eindhoven University of Technology Library. Performance Improvement of Professional Printing Systems: from theory to practice / by Mohamed Ezzeldin Mahdy Abdelmonem. Eindhoven : Technische Universiteit Eindhoven, 2012 Proefschrift. ISBN: Copyright c 2012 by Mohamed Ezzeldin Mahdy. This thesis was prepared with the L A TEX documentation system. Cover Design: Verspaget & Bruinink, Eindhoven, The Netherlands.

4 iii Summary Markets demand continuously for higher quality, higher speed, and more energy-efficient professional printers. In this thesis, control strategies have been developed to improve the performance of both professional inkjet and laser printers. Drop-on-Demand (DoD) inkjet printing is considered as one of the most promising printing technologies. It offers several advantages including high speed, quiet operation, and compatibility with a variety of printing media. Nowadays, it has been used as low-cost and efficient manufacturing technology in a wide variety of markets. Although the performance requirements, which are imposed by the current applications, are tight, the future performance requirements are expected to be even more challenging. Several requirements are related to the jetted drop properties, namely, drop velocity, drop volume, drop velocity consistency, productivity, and reliability. Meeting the performance requirements is restricted by several operational issues that are associated with the design and operation of inkjet printheads. Major issues that are usually encountered are residual vibrations in and crosstalk among ink channels. This results in a poor printing quality for high-speed printing. Given any arbitrary bitmap, the main objective is to design actuation pulses such that variations in the velocity and volume of the jetted drops are minimized. Several model-based feedfoward control techniques using an existing model are implemented to generate appropriate input pulses for the printhead. Although the implementation of the model-based techniques shows a considerable improvement of the printhead performance compared with the current performance, further improvements are still necessary. We observe that besides the pulse shape the state of the ink surface at the nozzle plate (speed, position) at the start of the pulse influences the drop velocity considerably. This state at firing depends also on previous pixels in the bitmap of the image. Consequently, any pulse design has to guarantee almost the same initial state when firing a drop. Based on these facts, a model-free optimization scheme is developed to

5 iv Summary minimize the drop velocity variations taking into account the bitmap information. Experimental results show the effectiveness of the optimized pulses. Laser printing systems are highly depending on the appropriate combination of several design factors so as to become functional in a desired working range. The physical printing process involves multiple temperature set points at different places, precise electro-magnetic conditions, transfer of toner through certain pressures and layouts, and many other technical considerations. In the laser printing system there are several challenging issues and unknown disturbances. They originate from different sources, such as the printer itself (unknown phenomena appear, disturbances that are not foreseen, wear, contamination, failures, bugs), the environment of the system (power supply variations, temperature, humidity, vibrations), and the printing media (weight, coating, thermal properties, humidity characteristics, and initial temperature). These issues have a negative effect on the stability and performance of the laser printing system. The objective is to design a control scheme to achieve printing quality requirements and a high productivity. Good printing quality means that the fusing temperature should track a certain reference signal at different operating conditions. Based on the printing system behavior, we propose two different control schemes to cope with the large parameter variations and disturbances, namely, a Model Reference Adaptive Controller (MRAC) and a nonlinear (scheduled) observer-based output feedback control scheme. Both control techniques yield considerable performance improvements compared with the present industrial controller.

6 v Table of Contents Summary Table of Contents iii v 1 Introduction Professional printing systems Research targets Methodology and main contributions Thesis outline Drop-on-Demand Professional Inkjet Printer Inkjet printing technologies DoD piezoelectric inkjet printer Operational issues Experimental setup Objectives Control limitations Methodology Model-Based Feedforward Control for a DoD Inkjet Printhead Introduction Inverse-based control Control objectives Printhead model Single-channel feedforward control Multi-channel control Conclusions Experimental-Based Control for a DoD Inkjet Printhead Introduction Input pulse parametrization

7 vi Table of Contents 4.3 Experimental-based optimization Multi-channel control Bitmap-based control Conclusions Professional Laser Printers Introduction Development of laser printer Description of the printing system Printing system heat flow Control challenges for the printing system Improved Convergence of MRAC Designs for Laser Printer Introduction Preliminary Nonlinear time varying adaptation gain Multiple-adaptation gain MRAC design Numerical comparison Application of MRAC for laser printing system Conclusions RobustL 2 Control for a Professional Printing System Introduction Problem formulation Robust state feedback control Robust output feedback control LMI formulation for control synthesis Simulation example Robust control of professional laser printing system Conclusions Conclusions and Recommendations Conclusions Recommendations Bibliography 151 Acknowledgments 159 Curriculum Vitae 161

8 1 Chapter 1 Introduction This work has been performed as a part of the Octopus project. This project was a cooperation between Océ Technologies, the Embedded Systems Institute, Eindhoven University of Technology, and seven academic partners. The main goal of this project is to define new techniques, tools, and algorithms to design professional printers, which adapt themselves to cope with changes that occur during operation. Printers and paper reproduction systems need to make on-line trade-offs between several system aspects so as to guarantee the performance of the system. By doing so, different demands of the customers can be optimally met in real-time using the same machine.

9 2 INTRODUCTION 1.1 Professional printing systems The market of professional printing systems is a segment where Océ plays a dominant role with systems that produce, distribute, and manage documents. Documents are printed in color or black and white and in a variety of formats, see Figure 1.1. The Océ customers are typically working in offices, education, industry, or the graphics industry. As such, the market of Océ starts at the top of the low cost office printers and ranges up to the offset lithography printers. Faster, better quality, and lower costs of ownership are the main challenges for the development of professional printing systems. Recent advances in printing technology over the past few decades have made printing systems commercially available for home and office environments, with industry constantly pushing the limits in terms of productivity, accuracy, resolution, minimizing disturbance levels, reliability, and finding new applications. These printers depend on a wide range of deposition methods such as thermal and piezoelectric inkjet, and laser printing. Figure 1.1: Various professional printers developed at Océ. Several applications in industry are using inkjet printing technology due to its ability

10 1.2. RESEARCH TARGETS 3 to jet ink drops with variable size. In addition, it has shown potential for applications outside the document printing market due to its non-contact method of depositing ink or material droplets. The fundamental requirement in all industrial printing applications is disposing and precise positioning of very small volumes of ink, typically picoliters, on a printing medium. As inkjet applications grow, various types of jetting materials are required to be precisely dispensed from the inkjet printhead. Moreover, jetting performance needs to be efficiently controlled to make inkjet technology viable in various applications. However, during the jetting process several operational issues are encountered in the printhead, namely, residual vibrations and crosstalk. These operational issues result in large variations in the jetted drop properties, drop velocity and drop volume. Obviously, these variations limit the printhead performance. To improve the printhead performance with respect to drop velocity and drop volume, the actuation input for the printhead has to be properly designed. The designed actuation pulse should be able to achieve desired drop properties independent of the operational issues, jetting frequency, and bitmap to be jetted. Successful design for the actuation input requires understanding of the basic physics of drop formation and how the actuation input influences this jetting performance. The interactions between individual drops and the printing media as well as between adjacent drops are important in defining the resolution and accuracy of printed objects. Similarly, the key challenges of professional laser printers are to produce printed documents with the appropriate printing properties at acceptable price with high productivity and accuracy. The professional printing market has a high demand on print consistency and print quality. There are many external and internal parameters that influence consistency and quality (e.g. humidity, temperature, speed) and they have to be controlled. To introduce new and exciting applications, the printing system should be able to handle a wide range of media with an appropriate performance. An increasing range of paper sizes, weights, color, texture and finishing is required. Complex printing jobs might include multiple media types in one pass requiring a wide media range which can run concurrently in a print job. To meet these challenges, the printing system should be able to print with variable speed and on a wide variety of printing media. 1.2 Research targets The thesis is divided into two main parts: a drop-on-demand inkjet printing system and laser color printing. The first case tackles the operational issues, residual vibrations and crosstalk, encountered in a drop-on-demand inkjet printing system.

11 4 INTRODUCTION These operational issues limit now the attainable performance of the printhead. Large variations in the drop properties result as a consequence of varying the jetting frequency and the bitmap. That results in the following research goal, 1. Design simple actuation pulses for an arbitrary bitmap and a range of jetting frequencies such that the resulting drop properties are similar under all conditions. The second part of this thesis focuses on laser color printing. Laser printers have to produce high quality prints, have a high throughput, have to be reliable under a large range of conditions, and yield a low per-print cost. As a result, such printers should be adaptable with respect to variations in media, and the environmental variations. These challenges pose the following research goals, 1. Achieve accurate temperature control within a constrained real-time environment with fast and large parameter variations. 2. Design a control system that incorporates the available information about the print job to maximize throughput while satisfying in all situations quality constraints. 1.3 Methodology and main contributions Inkjet printing system The operational issues are large, but they are also reproducible and predictable. There are rather accurate models, but no sensors available for real-time measurements. Therefore, feedforward control is suitable for designing the actuation pulse. In this thesis, two different feedforward approaches are investigated. Firstly, an inverse-based feedforward control is implemented to deal with the residual vibrations and crosstalk. Inverse-based control is successfully used for high-precision application since it has the ability to perfectly track a desired trajectory with high precision. That makes this control strategy very appealing in our application. We explore different possibilities of the inverse control to cope with the residual vibrations and crosstalk. To overcome the modeling problems that usually degrade the performance of the modelbased feedforward control, an experimental-based feedforward control is proposed. In this approach, the actuation pulse is optimized based on the measured drop properties. The optimization is carried out with a printhead in the loop. Therefore, all modeling issues are avoided. The main advantage of this approach is that the feedforward input

12 1.3. METHODOLOGY AND MAIN CONTRIBUTIONS 5 is designed based on the drop properties, which are the main measure for the printing quality, and not on an intermediate variable. By understanding the physics of a printhead, a simple structure of the actuation pulse is suggested. This structure allows a simple optimization and opens a possibility for real-time pulse adaptation if measurements become available. We show throughout the thesis that designing the proper pulse will considerably improve the printhead performance without redesigning the existing printhead Laser printing system Based on the research goals and the analysis of existing control strategies show that gain scheduling, adaptive control and/or robust control are appropriate strategies. As we know the changing parameters, robust control will be too conservative yielding less performance. For adaptive control the emphasis has to be focused on fast adaptation rate. Adaptive control is a very powerful tool when the system dynamics are time varying. The main difference between adaptive control and robust control is that adaptive control does not need any priori knowledge about the bounds on these uncertain or time-varying parameters. Robust control guarantees that if the changes are within given bounds the control law need not be changed, while stability is guaranteed. Adaptive control is concerned with control laws, which adapt themselves. The large and fast variations in the printing system require adaptive controllers with a short adaptation phase. Therefore, we propose two methods to improve the adaptation convergence of the adaptive control. Since the main source of parameter variations is due to different printing jobs, which is known, gain scheduling is an appropriate choice to incorporate this knowledge. Once an operating point is detected, the controller parameters are changed to the appropriate values, which are obtained from the precomputed parameters set. Transitions between different operating points, which lead to significant parameter changes, are handled by interpolation or by increasing the number of operating points. Thus, the gain scheduler consists of a look-up table and the appropriate logic for detecting the operating point and choosing the corresponding values of the controller parameters from the table. Adaptive control and gain scheduling are both used to adapt the printing system to physical runtime variations and to optimize the system to the different and changing preferences of the user.

13 6 INTRODUCTION 1.4 Thesis outline Part I : Professional Inkjet Printing System In chapter 2, we start with a historical overview about the development of inkjet printing systems. We explain the basic principles and the structure of the printhead under investigation. That leads to a discussion over the operational issues that degrade the performance of the printhead. We present an experimental setup, which is used to study the printhead. Finally, we indicate the main industrial and research challenges and a short overview about the methods to achieve these objectives. In chapter 3, we present the application of the inverse-based feedforward control to cope with the residual vibrations and crosstalk in the inkjet printer. We start with exploring the basics of the model-based inverse control and with formulating the control objectives. Finally, the application of the feedforward control to single and multi channel(s) with simulation and experimental results are described. In chapter 4, an experimental-based control strategy is developed to reduce the effect of the residual vibrations and crosstalk. A new parametrization of the actuation pulse is introduced. Based on physical understanding the dynamics of an ink channel, we define a solution: each pulse has to start with the same state (meniscus velocity and meniscus position). We formulate optimization problems to reduce the drop velocity variations for both single and multi channel(s). Finally experimental results show the effectiveness of the optimized pulses. Part II: Professional Laser Printing System In chapter 5, we present an overview of the laser printing system. A brief description of the printing process is given. We identify a set of challenging control problems that are relevant to the printing process. Consequently, we motivate the use of adaptive control to tackle these control problems. In chapter 6, model reference adaptive controller (MRAC) is selected to improve the behavior of the laser printing system. Two different methods to improve the convergence of the MRAC, namely, using a nonlinear varying adaptation gain and using multiple adaptation gains with a new adaptation law are addressed. Using a numerical example, the performance of the two methods are compared with the performance of the standard MRAC. Finally, the application of the proposed approaches for a printing system is illustrated. In chapter 7, a Takagi-Sugeno (T-S) model is proposed as a feasible approximation to the laser printing system. A robust control problem is formulated taking into account the approximation error. Based on the print job, state and output feedback controllers are designed. The application of this robust gain-scheduling control design to a professional printing system is discussed. In chapter 8, the conclusions and the recommendation of this research are presented.

14 7 Chapter 2 Drop-on-Demand Professional Inkjet Printer Drop-on-demand (DoD) inkjet printing is an efficient technology for depositing picoliter drops on various printing surfaces. DoD technology is compatible with various liquids and does not require contacting the printing media. DoD inkjet printing combines several advantages including high speed, quiet operation, and compatibility with a variety of printing surfaces. Moreover, with DoD printing one can make patterns without any additional lithographic processes. Inkjet printing can reduce the number of processing steps compared to conventional patterning processes. This results in a lower production cost in manufacturing. Besides the well known small inkjet printers used as home or office appliances, professional inkjet printers are widely used in industry. Nowadays, DoD inkjet technology is applied in many engineering and scientific applications, see Figure 2.1. Inkjet technology is not only used for document printing, the production of posters, and CAD drawings but it is also applied in the electronics industry for the production of polyled displays and the production of biochips for medical research. In textile industry, wide-format inkjet printers are used to print on silk, cotton, and polyester. Inkjet technology plays also an important role in 3D printing of rapid prototyping [1]-[5].

15 8 DROP-ON-DEMAND PROFESSIONAL INKJET PRINTER Manufacturing Electronic Circuits DNA Sampling Blood Testing & Protein Analysis Textile printing with wide-format inkjet printers on silk, cotton, polyester Inkjet Decoration of Ceramic Figure 2.1: Various applications of Inkjet printing. 2.1 Inkjet printing technologies In inkjet technology, one distinguishes between continuous inkjet or drop-on-demand (DoD). For continuous inkjet printer, a continuous stream of ink is supplied to the printhead. DoD is a broad classification of inkjet printing technologies where drops are ejected from the printhead only when required. The drops are usually formed by the creation of pressure pulses within the printhead. The particular method that is used to generate these pressure pulses creates the primary subcategories within DoD technology, namely, thermal, piezoelectric, electrostatic, and acoustic. In this section, we provide a short overview of the development of the inkjet technology. After that, we explain the basic mechanisms of different inkjet technologies History of inkjet technologies In 1878, Lord Rayleigh described the basic principles of how a liquid stream breaks up into drops [6]. However, it took several decades before implementing these physical principles into a working device. The first device based on these principles was developed in 1948 by Siemens Elema in Sweden [7]. This device was similar to a galvanometer. Instead of using a pointer as an indicator, a pressurized continuous stream of ink was used to record the signal onto a transported recording media.

16 2.1. INKJET PRINTING TECHNOLOGIES 9 In the early 1960s, the principle of continuous inkjet printing was established. By applying a pressure wave pattern, the ink stream is splitted into drops of uniform size and spacing [8]. After breakoff, an electric charge is imposed on the drops. While passing through an electric field, the uncharged drops are deflected into a collector for recirculation, whereas the remaining charged drops are disposed directly onto the media to form an image. In the 1970s, IBM launched a development program for continuous inkjet technology [9]. In the late 1970s, the first DoD inkjet technology appeared. A DoD printer ejects ink drops only when these drops are used in imaging on the media. Many DoD inkjet systems were invented, developed, and produced commercially in the 1970s and 1980s, including the Siemens PT-80 serial character printer [10]. In these printers, a voltage pulse causes ink drops to be ejected as a result of a pressure wave created by mechanical motions of piezoelectric ceramic actuators. In 1979, Canon invented a mechanism, called the bubble jet, where ink drops are ejected from the nozzle by the expansion of a vapor bubble on the top surface of a heater located near the nozzle [11]. At the same time, Hewlett-Packard developed a similar inkjet technology called ThinkJet (thermal inkjet) [12]. This development was the first low-cost inkjet printer based on the bubble jet principle. Since the late 1980s, thermal inkjet or bubble jet printers became the practicable alternative to impact dot-matrix printers for home and office use, mainly because of their color capabilities, small size, low cost, and quietness. For more details about the history of inkjet technology development, see [13]-[16] Inkjet technology map Inkjet printing has been implemented in many different designs and has a wide range of potential applications. A basic overview of inkjet technologies is shown in Figure 2.2. Inkjet printing technologies are divided into the continuous and the DoD inkjet methods. The basic mechanism of the continuous printing technology is to pump fluid from a reservoir to small nozzles, which eject a continuous stream of drops at high frequency, typically from 50 khz to 175 khz, using a vibrating piezoelectric crystal. The drops are electronically charged by passing them through a set of electrodes. The charged drops then pass a deflection plate that uses an electrostatic field to deflect the drops that will be printed. Undeflected drops are collected and returned for re-use. As depicted in Figure 2.3, in this deflection methodology, the continuous inkjet is de-

17 10 DROP-ON-DEMAND PROFESSIONAL INKJET PRINTER Inkjet Technology Continuous Drop-on-Demand Binary Deflection Multiple Deflections Thermal Electrostatic Piezoelectric Acoustic Roof -Shooter Side -Shooter Bend Mode Squeeze Tube Push Mode Shear Mode Figure 2.2: Inkjet technology diagram. signed as a binary or multiple deflection system that separates drops for print from drops that are recollected and not printed. In a binary deflection system, the drops are either charged or uncharged. The charged drops are disposed directly onto the media, while the uncharged drops fly into a gutter for recirculation. In a multiple deflection system, drops are charged and deflected to the media at several levels. The uncharged drops pass straight to a gutter from where the ink is recirculated. Also the DoD inkjet printers eject ink drops as a result of an electric signal, but only when needed. Depending on the actuator, the DoD printing technology is classified into thermal and piezoelectric. In the thermal process, drops of ink are forced out of the nozzle by heating a resistor to C, which causes a thin film of ink above the heater to vaporise into a rapidly expanding bubble. Depending on its configuration, a thermal inkjet is either a roof-shooter with an orifice located on top of the heater, or a side-shooter with an orifice located on a side nearby the heater, see Figure 2.4. The advantages of thermal inkjet include the high nozzle density and potential for very small drop sizes. High nozzle density leads to compact devices, potentially, highresolutions, and low printhead costs. On the other hand, the drawbacks of this technology are mainly related to the limitations of the fluids that can be used. The fluid has to contain a substance that can be vaporized at reasonable temperatures and has to withstand the effects of high temperatures. Moreover, these high temperatures can form a hard coating on the resistive element, which degrades its efficiency and, ultimately, the life of the printhead. Nowadays, professional and industrial inkjet printers use a piezoelectric actuator in an

18 2.1. INKJET PRINTING TECHNOLOGIES 11 HV Drop generator Charge Elecrode High voltage deflection plate Printing media Gutter (a) Binary-deflection system HV Drop generator Charge Elecrode High voltage deflection plate Gutter Printing media (b) Multiple-deflection system Figure 2.3: Continuous inkjet printer configurations. Printing Media Orifice Printing Media Heat Sink Nozzle Layer To Ink Supply Bubble Heater Heater Substrate Barrier Layer To Ink Supply Heater Bubble Heater Substrate Heat Sink 1. Roof-shooter thermal inkjet 2. Side-shooter thermal inkjet Figure 2.4: DoD thermal inkjet printer configurations.

19 12 DROP-ON-DEMAND PROFESSIONAL INKJET PRINTER ink-filled chamber behind each nozzle instead of a heating element. By applying a voltage, the piezoelectric material changes its shape or size, which generates a pressure pulse in the fluid forcing a drop of ink to leave the nozzle. Based on the piezoelectric actuator deformation mode, the piezoelectric technology is classified into four main types, namely, squeeze mode, bend mode, push mode, and shear mode, see Figure 2.5. For squeeze mode, radially polarized ceramic tubes are used. In both bend and push mode design, the electric field is generated between the electrodes parallel to the polarization of the piezoelectric material. In a shear mode printhead, the electric field is designed to be perpendicular to the polarization of the piezoelectric actuator. A piezoelectric inkjet printer allows a wide variety of fluids in a highly controllable manner and high reliability with a long life for the printhead. However, the printheads are expensive, which limits the applicability of this technology in low-cost applications. 2.2 DoD piezoelectric inkjet printer In this thesis, we focus on a DoD piezoelectric inkjet printhead, which consists of ink channels with a high integration density. Each channel is equipped with its own piezoelectric actuator. The ink in the channel is supplied from a reservoir, which is located above the channels. Filters ensure that no unwanted particles enter the ink channels. An actuator foil covers the ink channels in the channel block. The foil is connected to the actuator plate with piezoelectric elements and substrate. The nozzle plate, which contains the nozzles, is mounted to the bottom of the head. The part of the head between a channel and a nozzle is called the connection. In Figure 2.6, an exploded view of the piezoelectric inkjet printhead is shown together with a schematic representation of a single channel Printhead dynamics The fluid dynamics in the ink channel is governed by the wave propagation equation [15]-[16]. Consider the one-dimensional linear wave equation and 2 P x P ν 2 = 0, (2.1) t2 2 ζ x ζ ν 2 = 0, (2.2) t2

20 Piezoelectric acutator 2.2. DOD PIEZOELECTRIC INKJET PRINTER 13 (a) Squeez Mode (b) Bend Mode Diaphragm Ink Piezo Ceramics Piezo Ceramics Ink (c) Push Mode (d) Shear Mode Piezo Ceramics Diaphragm Piezo Ceramics Ink channel Ink Nozzle Figure 2.5: DoD Piezoelectric inkjet printer modes. Ink filter (a) Single channel Ink Ink channel (b) Overview of an inkjet printhead Filter Channel plate Ink Reservoir Filter Channels Connection Actuator foil Piezo fingers Nozzles Nozzle Ink drop Printing media Figure 2.6: Schematic representation of a single channel (a) and overview of a piezoelectric inkjet printhead (b).

21 14 DROP-ON-DEMAND PROFESSIONAL INKJET PRINTER with x [0,L], t 0, that describes the pressure P(x,t) and the particle displacement ζ(x,t) in a medium of a one-dimensional channel, where ν is the sound speed in the medium and L is the length of the channel. The relation between the pressure P and the displacement ζ is given by P = ρν 2 ζ x, (2.3) withρthe fluid density. Suppose that the sound speedν is a constant, then each solution of (2.1) can be written as P(x,t) = f(x νt)+g(x+νt), (2.4) where f and g are two twice-differentiable functions. The pressure inside the channel is therefore the sum of two pressure profiles. The pressure wave f travels in the positive direction of the x-axis with velocityν, while the pressure waveg travels in the negative direction of the x-axis with velocity ν. When an obstruction occurs at some location inside a channel, part of the pressure wave is transmitted and part is reflected. A reflection coefficient describes either the amplitude or the intensity of a reflected wave relative to an incident wave. The reflection coefficient is closely related to the transmission coefficient. The simplest cases to analyze are the idealized open and closed ends. These assumptions are also appropriate for the end conditions in the DoD inkjet channel, where the side on which the nozzle plate is attached can be modeled as closed, since the nozzle opening is a negligible fraction of the channel cross-sectional area. The reservoir side can be considered as open, since the inside diameter of the reservoir is considerably larger than the inside diameter of the channel. The pressure reflections from open and closed ends are obtained from the boundary conditions with the use of (2.1) and (2.3). Consider first the open end, where the (left) boundary condition of (2.1) is assumed to be zero pressure P(0, t) = 0. This boundary condition is satisfied by superimposing a similar pressure wave of opposite sign on the incident pressure wave. This pressure wave is traveling in the opposite direction at the same distance from the end as the incident wave. On the other hand, for the closed end the boundary condition is zero velocity ζ t (L,t) = 0. Since the displacement ζ(x,t) satisfies the same wave equation as the pressure (2.1), it follows that the velocity also satisfies a similar equation. Hence, displacement and velocity have propagating wave solutions similar to (2.4). Therefore, when the wave reflects from an open end, the phase of the reflected wave is the same

22 2.2. DOD PIEZOELECTRIC INKJET PRINTER 15 Printing media Piezoelectric acutator Ink drop Input Pulse Time Figure 2.7: Drop jetting mechanism. phase of the incident wave. A wave pulse reflects from an open end with the opposite phase as the incident wave. According to the above analysis, a trapezoidal pulse is applied to the piezoelectric actuator to fire a drop, as shown in Figure 2.7. Then, ideally, the following occurs. First, a pressure distribution is generated in the channel by enlarging the volume in the channel. The initial pressure profile splits and propagates in both directions. These pressure waves are reflected at the reservoir that acts as an open end and at the nozzle that acts as a closed end. A negative pressure profile reflects at the nozzle and causes the meniscus to retract. The meniscus is the curve in the upper surface of the ink close to the surface of the nozzle. Next, by decreasing the channel s volume to its original value, a positive pressure profile is superimposed on the reflected waves when these waves are located exactly in the middle of the channel. Consequently, the wave traveling toward the reservoir is canceled, whereas the wave traveling toward the nozzle is amplified such that the pressure is large enough to result in a drop Drop formation For simulating the drop formation the nonlinear Navier-Stokes equations have to be solved numerically. Usually, these models are 3D or 2D and computationally intensive. For a typical printhead, the drop formation process includes four main stages, as shown

23 16 DROP-ON-DEMAND PROFESSIONAL INKJET PRINTER in Figure 2.8 where red color reflects low pressure inside the channel, while blue color represents high pressure in the channel. First, the negative pressure inside the ink channel causes a retraction of the meniscus. This negative pressure is caused by the initial pressure wave that hits the channel nozzle interface, as explained in the previous section, see Figure 2.8A. As a result of the positive pressure wave that hits the channel nozzle, the meniscus velocity starts to increase and starts moving outside the nozzle without deformation. Then, the meniscus surface starts deforming in outward direction against the surface tension. The deformed area grows in both radial and axial direction. After that, the velocity of the ink reaches its maximum, see Figure 2.8B-C. As shown in Figure 2.8D, the pressure becomes negative again and the velocity of the meniscus starts to decrease. This causes a decreasing flow of mass and kinetic energy in outward direction. Due to the surface tension, necking of the drop s tail takes place at the tip of the nozzle. Finally, the velocity of the ink becomes negative, the tail breaks, and the drop is jetted. During this process the tail might break up, forming satellite drops. These satellites may or may not catch up with the main drop and merge, see Figure 2.8E. Satellite drops highly affect the printing quality. Therefore, the combination of ink properties, viscosity and surface tension, nozzle design and actuation pulse is tuned to create consistent drops without depositing satellites on the printing media. Figure 2.8: The drop formation process simulated by Flow3D.

24 2.3. OPERATIONAL ISSUES Printhead performance Although the performance requirements, which are imposed by the current applications, are tight, future performance requirements are expected to be even more challenging. Several requirements are related to the resulting drop properties, namely, drop velocity, drop volume, drop velocity consistency, productivity, and reliability. The resulting drops are required to have a certain velocity, typically around5 10 m/s. A high drop velocity results in a short time of flight. Therefore, the disturbance effects, such as variations in the printhead-printing media distance, are reduced, thus the dot position errors are smaller. Depending on the application, the performance requirement concerning volume typically varies from 1 to 25 picoliters. Some applications require that the drop size is varied during the operation. For instance, when large areas are needed to be covered, large drops are desired, whereas for high-resolution printing small drops are desirable. Consistency of drop velocity is a crucial issue for the printing quality. The variations in the drop velocity between successive drops and between the nozzles must stay within 1 m/s, to avoid irregularities and shadow effects in the printed object. The productivity of a printhead is mainly determined by the number of nozzles per inch and the jetting frequency. Jetting frequency is defined as the number of drops that a channel jets within a certain time, which is typically khz. Evidently, these two factors depend on the design of the printhead and the actuation signal. Reliability of the jetting process is one of the prominent performance requirements for printheads. Reliability is defined as the absence of nozzle failures per a certain number of jetted drops, a typical value for nozzle failure is once per million drops. 2.3 Operational issues Meeting the above performance requirements is severely disrupted by several operational issues that are associated with the design and operation of inkjet printheads. Major issues that are usually encountered are residual vibrations and crosstalk. We discuss this items next Residual vibrations After a drop is jetted, the fluid mechanics within an ink channel are not at rest immediately. Traveling pressure waves remain present. Figure 2.9 shows the time trajectory of the meniscus velocity when a standard trapezoidal actuation pulse is applied to the piezoelectric actuator. Usually, the fixed actuation pulse is designed under the assump-

25 18 DROP-ON-DEMAND PROFESSIONAL INKJET PRINTER tion that a channel is at rest. This assumption is apparently not satisfied for about 100 µs, see Figure 2.9, after the actuation pulse. The time needed for the residual vibrations to damp out is substantially larger than the short actuation time. This transient time in the residual vibrations limits the maximally attainable jetting frequency to 10 khz, and, therefore, the drop properties and even the stability of the jet process cannot be guaranteed at higher frequencies. These oscillations have significant consequences concerning the productivity and drop consistency of a printhead. The presence of residual vibrations highly affects the volume and the velocity of the subsequent drops being fired. Since the initial values of meniscus position and meniscus velocity play a crucial role in determining the velocity of the jetted drop, the residual vibrations result in a different initial meniscus position and velocity for the subsequent drops. To obtain acceptable drop characteristics with this fixed actuation pulse, the fixed actuation pulse is designed for a specific basic jetting frequency with a small range of frequencies around this basic frequency. To be more flexible and robust, the printhead must jet drops over a wider frequency range with the same or even improved drop properties. For a continuous jetting nozzle, the DoD frequency curve for the velocity, as shown in Figure 2.10, is obtained. The DoD curve describes the relation between the jetting frequency and the drop velocity. This curve demonstrates that, depending on the jetting frequency, positive or negative interference of the pressure waves results in a higher or lower drop velocity. As depicted in the figure, considerable velocity fluctuations result from the presence of the residual vibrations. The drop velocity varies from 2.5 to 13.5 m/s. Ideally, the drop velocity is required to be independent on the jetting frequency and to remain constant for all jetting frequencies, as shown in Figure Crosstalk A second phenomenon that is encountered in jetting is the interaction between different channels, this phenomenon is known as crosstalk. The crosstalk originates from the fact that the pressure waves within one channel influence the neighboring channels. This type of crosstalk is known as acoustic crosstalk. Another source of the crosstalk is the deformation of the channel. Since all piezoelectric fingers are connected to a substrate, a deformation of one piezoelectric actuator induces a deformation of the neighboring units. Consequently, the volume of the neighboring channels changes too, which induces pressure waves in the neighboring channels. The deformation of the printhead structure can originate from two sources. The first source is the result of a channel being actuated and is referred to as direct voltage crosstalk. The second source is the result of the occurring pressure wave that causes deformation of the channel and is called indirect or pressure crosstalk.

26 2.3. OPERATIONAL ISSUES v meniscus (m/s) Time (µs) V actuation (V) Time (µs) Figure 2.9: Simulated time response of the meniscus velocity on a fixed trapeziumshaped pulse Drop speed is required to be constant and independent of the DoD frequency 10 Drop speed (m/s) DoD frequency (khz) Figure 2.10: Drop-on-demand velocity curve of the standard pulse for different jetting frequencies.

27 20 DROP-ON-DEMAND PROFESSIONAL INKJET PRINTER The influence on the drop velocity of the center channel of an array of channels when neighboring channels are active is shown in Figure When the direct neighbor, channel 1 or -1, in particular, becomes active, the drop velocity of channel zero drops from 6 to 5 m/s. As shown, the effect of crosstalk on the drop velocity is substantial. Note that for channels located further away, the influence of crosstalk decreases. Optimally, the drop velocity is required to be constant and independent on the actuation of the neighboring channels. 2.4 Experimental setup A schematic overview of the experimental setup is depicted in Figure With this setup, inkjet printheads can be investigated in various ways. The input is the voltage applied to a piezoelectric actuator of the inkjet printhead. Two sensors are available in this setup. The piezoelectric element can be used not only as an actuator but also as a sensor to measure the pressure waves in the channel after jetting a drop, this signal is known as PAINT signal. A charge-coupled device camera, equipped with a microscope, is used to monitor the properties of the resulting drop. The ink drops are monitored by means of optical methods like stroboscopic illumination at drop formation rate and high-speed camera. The setup can be divided into a part, which controls the printhead and a part to visualize the drops. The required reference temperature is controlled by a PID controller. The printhead is mounted in the vertical direction with the nozzles faced down. An air pressure unit keeps the pressure in the ink reservoir 8 mbar below the ambient pressure to avoid that the ink flows out of the nozzles under the influence of gravity. As depicted in Figure 2.12, the setup is connected to a computer that is equipped with cards for image processing and communication. On this computer, the desired actuation signals can be programmed and relevant data can be stored and processed. After defining the actuation signal parameters, these parameters are sent to a waveform generator. The waveform generator sends the signal to an amplifier unit. From the amplifier unit, the signal is fed to a switchboard. The switchboard is controlled by a computer and determines which channels are provided with the appropriate actuation signals. An oscilloscope is used for tracing both the actuation and PAINT signals. This oscilloscope is connected to the computer and displayed data can be stored on the computer. 2.5 Objectives Residual vibrations and crosstalk result in large variations in the drop velocity and volume. In the current inkjet printers, a fixed actuation pulse is used. This pulse cannot

28 2.5. OBJECTIVES Drop speed has to be constant and independent of the actuation of neighboring channels 6 Drop speed of channel 0 (m/s) Active channels Figure 2.11: Influence on the drop velocity of channel 0 (center channel) by actuation of different neighboring channels at the same time. Switch board Actuation Pulse Amplifier Waveform generator Pressure unit Temperature control unit CCD Camera C Light Strobe Piezo sensor signal (PAINT) Oscilloscope Image Figure 2.12: Schematic diagram of the experimental setup.

29 22 DROP-ON-DEMAND PROFESSIONAL INKJET PRINTER cope with the mentioned operational issues that highly affect the print quality. Apparently, the state (both meniscus position and velocity) at the firing instant determines the drop velocity and drop volume. The state at firing depends also on the bitmap (pixels on/off). Differences in drop velocity cause drops to arrive at the printing media at unpredictable positions. Differences in volume lead to color density variations on the printing media. These variations result in ragged edges or banding, and therefore reduce print quality. The main objective in this study is to improve the performance of the printhead. In particular, we focus on drop velocity consistency and productivity. Thus, we want to minimize the velocity variations that occur due to the presence of the residual vibrations and crosstalk. This problem statement can be translated to the following objectives: 1. To reduce the drop-velocity variations for each nozzle at each jetting frequency ( 1 m/s) 2. To reduce the drop-velocity variations over all the jetting frequencies (flat DoD curve), it has to be less than 1 m/s over the frequency range khz. 3. To reduce the effect of the crosstalk. For any arbitrary bitmap, the maximum drop-velocity variation of the jetted drops has to be less than 1 m/s. Thus, given an arbitrary bitmap, our main objective is to design actuation pulses such that the same initial meniscus state at firing a drop is guaranteed. 2.6 Control limitations To achieve these objectives, the actuation pulse should be designed to damp the residual vibrations and minimize the crosstalk. There are several control techniques to design the actuation input. However, there are two basic restrictions that don t allow full control of the printhead. 1. No sensors are available for online measurements of any variable. Consequently, this excludes any possibility for feedback control. Since the printheads behave in a predictable way based on their physical designs, feedforward control can still be a suitable option. 2. Only certain classes of actuation inputs can be used, since only trapezoidalshaped pulses can be generated using the current driving circuits. This limits the control scope to a pulse shaping problem.

30 2.7. METHODOLOGY Methodology In chapter 3, a model-based control approach to design the jetting pulses is described. In this approach, an inversion-based feedforward controller is proposed, where the controller dynamics are chosen to be the inverse of the printhead dynamics. This cancels all system dynamics and yields an overall unity transfer function. This is the Perfect Tracking Controller (PTC) strategy. Hence, the actual drop velocity will be exactly the same as the desired input velocity. A common difficulty in realizing a PTC strategy, however, is that the PTC may produce unbounded or oscillatory outputs. This will occur when the transfer function of the system contains zeros that cannot be canceled. Two classes of zeros are regarded in this respect, unstable zeros (non-minimum phase or unstable inverse) and stable oscillatory zeros (oscillatory inverse). The former implies an unstable controller, while the latter might generate oscillatory control efforts reaching the actuator saturation levels. Since the dynamics of the printhead shows a non-minimum phase behavior, various feedforward control algorithms are presented in chapter 3. An optimal inversion method is used to cope with the residual vibrations and the crosstalk. In chapter 4, an experimental-based control is proposed with a printhead in the loop. The drop properties are measured using a high-speed camera. An image of the time history of the drops traveling from the nozzle plate to the printing medium is recorded. Based on this image, an image processing technique is developed to retrieve the actual velocity of each drop. The input pulse is optimized such the the error between the actual drop velocity and desired drop velocity is minimized. A novel jet pulse structure is proposed to cope with single channel residual vibrations, crosstalk, and even generalize optimization over each bitmap to be printed. Both approaches result in strongly reduced interactions. The results are experimentally verified and provide very valuable steps towards flexible and robust printing systems [33].

31 24 DROP-ON-DEMAND PROFESSIONAL INKJET PRINTER

32 25 Chapter 3 Model-Based Feedforward Control for a DoD Inkjet Printhead Feedback control is based on the ability to measure the controlled variable. In the inkjet printer, no sensors are available for online measurement of the system variables. Therefore, feedback control is not possible and a feedforward controller is the only appropriate solution for controlling the printhead. Although residual vibrations and crosstalk effects are large, these effects are lightly predictable and reproducible. Hence, a model-based feedforward controller can be appropriate for this case. With a rather good model of the dynamics of the printhead, the construction of a feedforward controller as the inverse dynamics of the plant is a reasonable choice. In this chapter, we present the implementation of an inverse-based feedforward controller to deal with the residual vibrations and crosstalk.

33 26 MODEL-BASED FEEDFORWARD CONTROL FOR A DOD INKJET PRINTHEAD 3.1 Introduction Model-based feedforward inversion of system dynamics is usually used to design inputs that achieve high-precision output tracking, this input is referred to as the inverse input. The inversion technique is applied to several output tracking applications, for example, aircraft control, high-precision positioning of piezoelectric probes, and robotic tracking control. Major difficulties in realizing a model-based inversion strategy are that the resulting controller may produce unbounded or oscillatory outputs. This problem occurs when the system is non-minimum phase. Moreover, the model-based inversion strategy is sensitive to model uncertainty. These difficulties have been addressed in the development of optimal-inversion techniques in [25]. In particular, the optimal-inversion technique proves useful to account for modeling errors by inverting only the system model in frequency regions, where the model uncertainty is sufficiently small [26]. Another challenge in implementing the optimal-inversion approach is that the resulting input tends to be noncausal [26]. This approach therefore requires the knowledge of the entire future trajectory of the desired output to compute the inverse input at the current time instant. The noncausality of the optimal input restricts the stable-inversion technique to trajectory-planning applications. This restriction is alleviated through the development of the preview-based approach to the stable-inversion technique [27], which obtains the inverse input by using a finitely previewed trajectory rather than the entire future desired trajectory. In this chapter, we present the application of the optimal inversion technique to cope with the residual vibrations and the crosstalk. We start with a review of the basics of the model-based inverse control. After that, we present the application of the feedforward control to a single channel with simulation and experimental results. Finally, multichannels inversion is addressed to cope with the crosstalk between the channels. 3.2 Inverse-based control As mentioned, inverse systems play an important role in feedforward control design. This section reviews the main principles of the inversion-based approaches to find feedforward inputs that improve the performance of the inkjet printhead. The existing models for the inkjet printhead are linear or can be linearized. Therefore, in this section we present the inversion problem of a linear system. Consider the linear time invariant system, ẋ(t) = Ax(t)+Bu(t), (3.1) y(t) = Cx(t)+Du(t), (3.2)

34 3.2. INVERSE-BASED CONTROL 27 where x(t) R n is the system state, and where the number of inputs is the same as the number of outputs, u(t) R m and y(t) R m. This implies that the system is square. The transfer matrix is given by G(s) = C(sI A) 1 B +D. (3.3) Definition A square rational function G(s) is invertible if there exist a square rational function H(s) (of the same dimension asg(s)) such that G(s)H(s) = H(s)G(s) = I for all s C. In case of non-square systems, the concept of a left inverse and right inverse is introduced. A left inverse ofg(s) is defined ash L (s), with the property thath L (s)g(s) = I. Similarly, the right inverse is defined ash R (s), with the property thatg(s)h R (s) = I. For feedforward control design, the right inverse is more valuable because u(s) := H R (s)y d (s) computes the input that, when applied tog(s), gives the outputy d. A nonsquare system has different number of inputs and outputs. If the number of inputs of G is larger than the number of its outputs, there is no unique solution for the right inverse problem dc-gain inverse The simplest feedforward method is dc-gain inversion, where the feedforward inputu ff is computed as u ff (t) = [G(0)] 1 y d (t), where y d is the desired output of G and G(0) := CA 1 B + D (assuming that A 1 exits) denotes the dc-gain of the system whose inverse (as a matrix) is assumed to exist here. This approach is suitable for slow desired trajectories, but results in a significant tracking error if the operating frequency is increased since the dynamics is not taken into account. Note that the maximum tracking error increases with both the amplitude of the desired trajectory as well as the frequency that needs to be tracked Pole-zero cancellation inverse If the system dynamics are stable and minimum phase, i.e there are no poles and zeros in the open right half of the complex plane, then the inverse feedforward is obtained by inverting the system dynamics U ff (s) = G 1 (s)y d (s). Note thatu ff (s) andy d (s) denote here the Laplace transforms ofu ff (t) andy d (t) An important issue with the exact inverse is that the inverse G 1 may not be proper. That

35 28 MODEL-BASED FEEDFORWARD CONTROL FOR A DOD INKJET PRINTHEAD means that for some entries of G 1, the order of the numerator is higher than the order of the denominator. If G 1 is non-proper, let R d be the minimal integer such that 1 s Rd G 1 (s) = [s R d G(s)] 1 is proper. We then define U ff (s) = [s R d G(s)] 1 Ŷ d (s) = [s R d G(s)] 1 s (R d) Y d (s), (3.4) seth(s) := [s R dg(s)] 1 andŷd(s) := s (R d) Y d (s). Therefore, the desired trajectory y d is assumed to be sufficiently smooth (at least R d times differentiable with respect to time). Based on this assumption, a proper exact inverse is obtained as U ff (s) = H(s)Ŷd(s). Note that if the system is non-minimum phase, H(s) will be unstable. Indeed the nonminimum phase system zeros at the right half plane become the unstable poles of H(s). Therefore, (3.4) will typically result in an unbounded feedforward input u ff over time for any desired non-zero trajectory y d Optimal inversion The inversion problem is presented as the minimization of a quadratic-cost function. For a sufficiently smooth desired output y d L 2 the optimal inversion problem is to minimize the following cost function, J(u) = 0 u(t) Ru(t)+[y(t) y d (t)] Q[y(t) y d (t)]dt, (3.5) where, R 0 and Q 0 are weighting matrices. Frequency domain solution The optimal inverse is obtained as a filter as developed in [27] that minimizes J. Suppose that the system (3.3) is invertible as a rational operator. Hence, there exists a rational transfer matrix G 1 (s) such that G 1 (s)g(s) = I. We assume that system (3.3) and its inverse are analytic on the imaginary axis. Define G opt (s) := [R+G (s)qg(s)] 1 G (s)q. (3.6)

36 3.2. INVERSE-BASED CONTROL 29 The feedforward control input u f f = u opt is defined using a filter G opt (s) and the desired output y d as U opt (s) = G opt (s)y d (s) (3.7) Therefore, this optimal input u opt (t) = L 1 (U o pt(s)) minimizes J(u). Assume that G opt (s) is proper, by proper choice ofr,q, the inverse filterg opt (s) can be decomposed into a stable and anti-stable part, where G opt (s) = G st opt(s)+g as opt(s), (3.8) G st opt(s) = C st (si A st ) 1 B st +D st, (3.9) G as opt(s) = C as (si A as ) 1 B as +D as, (3.10) with A st,b st,c st,d st and A as,b as,c as,d as represent the state space realizations of G st opt(s) and G as opt(s), respectively so and λ(a st ) C := {s C Re s < 0} λ(a as ) C + := {s C Re s > 0} The bounded solution to the optimal inversion problem is then obtained by convolving the desired outputy d with the stable part ofg opt forward in time and with the anti-stable part backward in time as indicated in the following lemma. Lemma Let the desired output y d L 2 be defined for t R, and G opt (s) is proper. Then the optimal inverse input u opt (t) that minimizes J for all time t (, ) is given by u opt (t) = u st opt(t)+u as opt(t), (3.11) with u st opt L 2,u as opt L 2 be defined by u st opt(t) = C st t u as e Ast(t λ) B st y d (λ)dλ+d st y d (t), (3.12) opt(t) = C as e Aas(t λ) B as y d (λ)dλ+d as y d (t). (3.13) Proof. the complete proof is given in [27] t

37 30 MODEL-BASED FEEDFORWARD CONTROL FOR A DOD INKJET PRINTHEAD The computation of the optimal inverse input (3.11) at a time t requires the knowledge of all future values of the desired output y d (unless G opt is stable). In particular, the computation of u as opt(t) in (3.13) requires knowledge of all future values of the desired output y d (t) for the time interval [t, ). For practical reasons, u as opt(t) is often approximated by truncating the integral in (3.13), by using the information of the desired output during finite time interval [t,t+t p ] û as opt(t) = C as t+tp t e Aas(t λ) B as y d (λ)dλ+d as y d (t). (3.14) Hence, with this approximation the finite-preview-based optimal inverse input is given by û opt (t) = u st opt(t)+û as opt(t). (3.15) Note that the finite-preview-based implementation leads to tracking errors. The tracking error can be made arbitrarily small by choosing a sufficiently large preview time T p. In addition, this approach is highly sensitive to model uncertainties. Optimal state-space solution The frequency domain solution method described in section assumes that the system is square (square G) and stable, and G opt is proper. This is not usually the case. Moreover, it ignores the role of initial conditions. With the state space solution these assumptions are not necessary. In this section, we present a generalized state space approach that minimizes the cost function (3.5), where the role of initial conditions is included and without any conditions on non-minimum phase zeros or stability. This approach is also valid for non-square systems and does not need to assume that G opt is proper. Theorem Let y d L 2 be the desired output. Then the optimal inverse input u opt (t) that minimizesj for all time t is given by where and u opt (t) = F 1 x(t)+f 2 p(t)+ly d (t), (3.16) F 1 := R 1 (B K +D QC), F 2 := R 1 B, L := R 1 D Q, R := R+D QD, K = K 0 is the solution of the algebraic Riccati equation (ARE) A K +KA (B K +D QC) R 1 (B K +D QC)+C QC = 0 andp(t) is the solution of (the anti causal) system ṗ = (A+BF 1 ) p+(c +F 1 D )Qy d, p( ) = 0.

38 3.2. INVERSE-BASED CONTROL 31 Proof. Consider the candidate Lyapunov function V(x,p) = 1 2 x Kx+x p. V = 1 2 (ẋ Kx+x Kẋ)+ẋ p+x ṗ, = 1 2 (Ax+Bu) Kx+ 1 2 x K((Ax+Bu)+((Ax+Bu) p+x ṗ, by completing the squares and using the ARE A K +KA (B K +D QC) R 1 (B K +D QC)+C QC = 0, we obtain after long mathematical manipulations, V = u Ru (y y d ) Q(y y d )+ 1 2 y d(q QD R 1 D Q)y d p B R 1 B p u+ R 1 (B K +D QC)x+ R 1 B p R 1 D Qy d 2 R +x (ṗ+(a B R 1 (B K+D QC)) p (C R 1 (B K+D QC) D )Qy d ). Now set ṗ+(a B R 1 (B K+D QC)) p (C R 1 (B K+D QC) D )Qy d = 0 ṗ = (A+BF 1 ) p+(c +F 1 D )Qy d, Then, the time derivative ofv with be V = u Ru (y y d ) Q(y y d )+ 1 2 u F 1x F 2 p Ly d 2 R y d(q QD R 1 D Q)y d p B R 1 B p, This equation can be written as u Ru+(y y d ) Q(y y d ) = 1 2 u F 1x F 2 p Ly d 2 R dv dt y d(q QD R 1 D Q)y d p B R 1 B p. Integrating both sides we obtain J(u) = 1 2 x o Kx o +x o p o + 1 u F 1 x F 2 p Ly d 2 R y d(q QD R 1 D Q)y d p B R 1 B p dt, 0 dt

39 32 MODEL-BASED FEEDFORWARD CONTROL FOR A DOD INKJET PRINTHEAD which is minimized for u = F 1 x+f 2 p+ly d. That completes the proof. Since the desired output is only known during finite time interval [0,T end ], an approximate solution on the time interval is given as with û opt (t) = F 1 x(t)+f 2ˆp(t)+Ly d (t), ˆp = (A+BF 1 ) ˆp+(C +F 1 D )Qy d, ˆp(T end ) = Data-based inversion For data-based inversion, the key point is to utilize the inverse of the system dynamics from the frequency-domain implementation scheme. A schematic diagram for the proposed approach is shown in Figure 3.1. If (U(jw),Y(jw)) is the frequency response data, then a data-based estimate of the system transfer function is G(jw) = Y(jw)U(jw) 1 w R (3.17) where Y(jw) and U(jw) are the frequency-domain representation of the system output and input respectively. The inverse frequency response of the system is obtained as follows H(jw) = U(jw)Y(jw) 1 w R (3.18) Let the desired output y d (t) be periodic and have finite energy, i.e. y d L 2. Then the inverse input can be calculated in the frequency-domain as U inv (jw) = H(jw)Y d (jw) (3.19) Finally the feedforward inverse input is transformed to the time-domain u inv (t) = F 1 (U inv (jw)) (3.20) withf 1 is inverse Fourier operator. This approach is based on measured data which makes it insensitive to model uncertainties. However, the measured data should be sufficiently rich to capture the system dynamics. The causality-related limitations in the model-based inverse control approaches do not exist with the data-based inversion control approach. Particularly, the data-based inversion approach utilizes the inverse of the system dynamics from a frequency-domain implementation scheme. Due to the properties of the Fourier transform, the inverse input (3.20) will be always bounded even in case of the inversion of a non-minimum phase system.

40 3.3. CONTROL OBJECTIVES 33 y d(t) Y Inverse Fourier d(jw) U inv(jw) u inv(t) y(t) G inv (jw) Fourier G(s) Transform Transform Data-based inverse controller Figure 3.1: Data-based inverse control. 3.3 Control objectives Our main concern is to improve the performance of an inkjet printhead with respect to productivity and drop-consistency. Improving the productivity is achieved by minimizing the effects of both the residual vibrations and the crosstalk. Drop-consistency is one of the most important performance issues. Currently, the drop-consistency requirement is only achieved at low jetting frequencies, khz. The jetting of any random bitmap yields large variations in the drop properties. These large variations originate from the residual vibrations and crosstalk, which are the major performance limiting factors when considering the drop-consistency. Apparently, improving both the productivity and drop consistency require minimization of the residual vibrations and crosstalk. An inversion-based feedforward controller is employed to reduce the effect of the residual vibrations and crosstalk by perfect tracking of the reference trajectory. 3.4 Printhead model Several analytical and numerical models, which describe the dynamics of the ink channel, are available in the literature [17]-[21]. In general, the numerical models are very accurate and they include high level of details. These models are usually finite element models in which the governing differential equations are numerically solved using complex meshes and numerical integration techniques. The main drawback of these models is that they have a very high computation time, typically 24 hours to analyze the jetting of one drop. That makes it not suitable for control design. On the other hand, analytical models are less complex since the governing differential equations are simplified to be solved analytically. Sometimes over-simplification results in models with poor accuracy while under-simplification leads to models with high complexity. Combined models that include both numerical and analytical models result in models with less computation time with a reasonable accuracy.

41 34 MODEL-BASED FEEDFORWARD CONTROL FOR A DOD INKJET PRINTHEAD Lumped-parameter model Lumped-parameter model adopts an equivalent electric circuit to describe the dynamics of the ink channel. This modeling technique is a useful and commonly applied analysis approach for designing piezoelectric inkjet systems. In this modeling framework, a single resonance is modeled with with a capacitor, resistor, and inductor in series. Additional resonances is included by placing additional capacitor-resistor-inductor sets in parallel. The inductance represents the inertia, which is related to the fluid mass, the capacitance is a measure of fluid energy storage, and elasticity and the resistance is associated with any losses causing energy dissipation in the fluid, typically viscous losses. Accurate determination of the equivalent circuit parameters requires either a physical prototype or an accurate computational model to provide the data. In this model, it is assumed that the characteristic wavelength is larger than all dimensions in a channel. That means that the fluid in the flow direction is uniform at any instant in time. This assumption implies that the time required to transmit a change in the applied electric field on the piezoelectric actuator to a change in the meniscus shape at the nozzle is negligible. In [20], a transmission line models of the piezoelectric actuator, fluid chamber, and nozzle is proposed. This model permit analysis without the wavelength limitation and provide the ability to analyze the approximate interaction between multiple resonances in the complete system. However, this model still has a limited accuracy. Furthermore, a prediction error in the system response and the resonance frequencies may result form the assumption that the loss mechanisms are isolated to a single resistance in the motional component per resonance Two-port model In [18], a two-port model is developed to describe the dynamics of the ink channel. This model employs the concept of bilaterally coupled systems. The ink channel is divided into subsystems, namely, reservoir, piezoelectric actuator, channel, connection, and nozzle. Each subsystem is modeled as a two-port system based on first principle modeling. To couple these subsystems, the Redheffer star product [24] is utilized. Consequently, the two-port model of an ink channel is obtained by connecting the subsystems and applying suitable boundary conditions.this model has less complexity and requires low computational time. However, due to the modeling error, this model can not capture the first resonance frequency of the channel dynamics, which is the most important resonance frequency. Moreover, this model does not consider the interactions between an ink channel and its neighbors Narrow-gap model The Narrow-gap model, proposed in [17], describes the dynamics of one ink channel based on the narrow channel theory. This model describes the dynamics of one ink

42 3.5. SINGLE-CHANNEL FEEDFORWARD CONTROL 35 channel from the piezoelectric input voltage to the meniscus velocity. It also describes the interactions between one channel and five neighboring ink channels from the piezo input voltageu(k) R m to the meniscus velocity y(k) R p. The derivation of the narrow channel equations is based on the Navier-Stokes equations of motion and a continuity equation. The continuity equation results from the balance between the change in mass and the flux of mass in a control volume. The Navier- Stokes equation, which is the continuum version of Newton s second law, relates the inertial acceleration of particles of a fluid with internal and external forces that affect the channel. In the narrow-gap model, the frequency response of the system is obtained using the swept sine technique. The frequency response of this model at a frequency ω 0 is computed based on solving the wave equations for a sinusoidal input with the same frequency ω 0. The frequency response is computed by repeating the same procedure over a frequency range. The frequency response of the printhead is obtained as shown in Figure 3.2. The detailed derivation of this model is given in [17]. This model has a relatively low complexity. Since there is no sensor available to measure the meniscus velocity, we could not validate this model. Therefore, we have to assume that this model represent the dynamics of the ink channel with a reasonable accuracy. 3.5 Single-channel feedforward control In [28], a model-based inverse feedforward controller is developed to design an input pulse for a single channel such that the initial values of the meniscus position and velocity are the same for all jetted drops. A reasonable assumption is that these initial values have to be zero at the starting of each input pulse. This is achieved by suppressing the residual vibrations. In this section, the optimal-inversion feedforward control is applied to damp the residual vibrations in one ink channel. For the inversion-based feedforward controller synthesis, a lower order transfer function is identified to fit the frequency response of the printhead, see Figure 3.3. Both simulation and experimental results are performed to investigate the performance of the proposed inverse control inputs and to compare with the performance of the currently used standard input pulse. The choice of the reference meniscus velocity is a crucial issue since it is the link between the performance objectives and the adopted control objectives as explained in section 3.3. The drop properties highly depend on the meniscus velocity trajectory. However, it is not easy to find the relation between the resulting drop properties and the meniscus trajectory. Moreover, different meniscus trajectories might result in drops with similar properties due to the high nonlinearity, which is introduced by the jetting mechanism. Two important issues should be considered in the design of the reference meniscus trajectory. First, the reference trajectory should allow the refill of the channel, which requires not immediately to bring the channel at rest after the jetting of the drop.

43 36 MODEL-BASED FEEDFORWARD CONTROL FOR A DOD INKJET PRINTHEAD Phase (deg.) Magnitude (db) G 11 (z) G 12 (z) G 13 (z) G 14 (z) G 15 (z) G 16 (z) Frequency (rad/sec) Figure 3.2: Frequency response of the narrow gap model. Mapping piezo voltage as input to meniscus velocity as output. 0 Magnitude (db) Phase (deg) Frequency (rad/s) Figure 3.3: Frequency response of the narrow-gap model (dash-line) and the fitted transfer function (solid-line).

44 3.5. SINGLE-CHANNEL FEEDFORWARD CONTROL Desired meniscus velocity (m/s) Part 1 Part Time (µs) Figure 3.4: Reference meniscus velocity. Secondly, the fluid dynamics should be brought gradually at rest to avoid a high input voltage. Therefore, as shown in Figure 3.4, the reference meniscus velocity is chosen to contain two parts, the first part determines the drop properties, drop velocity and volume, which are computed based on the response of the standard trapezoidal pulse. The second part is responsible for refilling the channel and after that the meniscus velocity is forced to settle at zero, to ensure zero initial condition of the subsequent drops. With the perfect tracking of the feedforward inverse control, the residual oscillations are damped out in time before the next pulse Simulation results In this section, a SISO inversion-based feedforward control is implemented based on the narrow-gap model. Note that an ink channel shows a non-minimum phase behavior, which can be observed in Figure 2.9. Therefore, we implement the optimal inverse controller, as explained in section Based on the optimal tracking of the feedforward inverse control, the residual oscillations will be damped out. The synthesis of the inversion-based feedforward controller includes identification of a lower order transfer function to fit the frequency response of the printhead, as shown Figure 3.3. The identified transfer function of the ink channel has an order of 16 and 4 non-minimum phase zeros.

45 38 MODEL-BASED FEEDFORWARD CONTROL FOR A DOD INKJET PRINTHEAD We compare both the model-based input with the standard pulse in Figure 3.5. The feedforward input includes an additional negative pulse, which brings the channel to rest at20 25µs. On the other hand, fluid dynamics take around100µs to settle using the standard pulse. Thanks to the feedforward input, the attainable jetting frequency is increased to 50 khz compared with 10 khz. For frequencies higher than 50 khz, overlapping of the input is needed. Figure 3.6 shows the simulation results of jetting 10 drops at 40 khz. For the standard pulse, the meniscus velocity does not quickly come to rest after jetting a droplet. Therefore, the initial meniscus state is non-zero before jetting the next pulse. This causes a difference in the velocity profiles of the subsequent drops, which is observed in Figure 3.6. As explained earlier in this chapter, the meniscus trajectory is a major feature and a changed meniscus velocity will result in drops having different velocities. The feedforward inverse inputs are able to highly damp the residual oscillations and ensure the same initial meniscus state for all subsequent drops. The difference in the velocity profiles of the proposed inverse input is negligible. Consequently, this controlled scheme will result in consistent drop properties for all drops Experimental results The simulation results show that a considerable improvement can be achieved by implementing the feedforward inverse control. Thus, the proposed inverse feedforward control is applied to a real printhead and the results are compared with a standard pulse. We have fitted the feedforward input to a trapezoidal waveform. Since any arbitrary waveform can be generated using the waveform generator, we have applied both the original and fitted waveform. Both waveforms show very similar results. Therefore, we present here only the experimental results of the fitted waveform. The time history on the time interval [0,T] of the drop traveling form the nozzle plate to the paper are collected to analyze the performance of the printhead. Several experiments are carried out for various jetting frequencies ranging from 20 to 70 khz and the performance of the printhead is analyzed in terms of the drop velocity. The drop velocity of jetting 10 drops over jetting frequencies khz is depicted in Figures , for the standard pulse and the model-based feedforward inverse input, respectively. The model-based feedforward input shows less drop velocity variation compared to the standard pulse. The performance is evaluated based on the maximum drop velocity variation over the whole range of the DoD frequencies, the behavior of the first drop, and the maximum drop velocity variation at each DoD frequency.

46 3.5. SINGLE-CHANNEL FEEDFORWARD CONTROL 39 6 Meniscus velocity (m/s) y inv y st u inv 20 u st Piezo input (V) Time (µsec) Figure 3.5: System response for jetting one drop (simulation). 8 Meniscus velocity (m/s) y opt y st Piezo input (V) u opt u st Time (µsec) Figure 3.6: System response for jetting 10 drops at 40 khz (simulation).

47 40 MODEL-BASED FEEDFORWARD CONTROL FOR A DOD INKJET PRINTHEAD drop1 drop2 drop3 drop4 drop5 drop6 drop7 drop8 drop9 drop Drop speed (m/s) m/s DoD frequency (khz) Figure 3.7: Jetting 10 drops at different DoD frequencies, khz using the standard pulse. Drop speed (m/s) drop1 drop2 drop3 drop4 drop5 drop6 drop7 drop8 drop9 drop10 3 m/s DoD frequency (khz) Figure 3.8: Jetting 10 drops at different DoD frequencies,20 70 khz using the modelbased feedforward pulse.

48 3.6. MULTI-CHANNEL CONTROL 41 For the standard pulse, the drop velocity varies from 2 to 13.5 m/s, which is a considerable variation over the whole DoD frequencies. Figure 3.7 shows that the first drop behaves in a completely different manner compared to the subsequent drops. At 65% of the frequencies, the first drop is faster than the remaining drops. As a consequence, a poor printing quality is obtained and a shadow appears in the printed bitmap. Moreover, the maximum drop velocity variation at each jetting frequency is around 3 m/s, which is calculated as with with v max = max v(f). (3.21) f v(f) = v max (f) v min (f), (3.22) v max (f) := max t [0,T] v(t,f), v min (f) := min t [0,T] v(t,f). By applying of the model-based feedforward pulse, the drop velocity variation over the whole frequency range is reduced from 12 to 3 m/s. As depicted in Figure 3.8, the first drop behaves in a similar manner as the remaining drops. At each DoD frequency, all the drops have similar velocity. We compute the maximum drop-velocity variation based on (3.21) and it is less than 1.5 m/s. The simulation results show very small variations in the drop velocity. That implies a flat DoD curve and less drop-velocity variations at each jetting frequency. However, the experimental results shows 3 m/s variations in the DoD curve. That is due to modeling errors and unmodeled dynamics. Improving the printhead model will result in a better pulse design and therefore less drop-velocity variations. 3.6 Multi-channel control In this section, a MIMO inverse control is implemented for a DoD inkjet printhead. The narrow-gap model is utilized for MIMO inverse feedforward control synthesis purpose, since it describes the dynamics of six ink channels from the piezo input voltageu(k) R m to the meniscus velocity y(k) R p. The frequency response of this model is shown in Figure 3.2. A low order stable transfer matrix G(z) is identified to fit to the frequency response obtained from the narrow-gap model. The accompanying transfer

49 42 MODEL-BASED FEEDFORWARD CONTROL FOR A DOD INKJET PRINTHEAD function G(z) and from the piezo input voltage u(k) to the meniscus velocity y(k) is denoted as: G 11 (z) G 12 (z) G 1m. G(z) =.... (3.23) G i1 (z) G ii (z) G im (z) G p1 (z) G mm (z) and satisfies Y(z) = G(z)U(z) (3.24) where G ii (z) represents the dynamics of channel i, G ij (z), j i denotes the transfer function form the input of the channelito the output of channelj, andm = p = 6. The transfer function (3.23) is discretized from the continuous model with sampling interval 0.1µsec. According to the assumption that all channels are identical and symmetric, the transfer matrix G(z) is symmetric i.e. G ij (z) = G ji (z) and diagonal terms are the same i.e. G ii (z) = G jj (z) fori j. Figure 3.4 shows the reference meniscus velocity for one drop for one channel. If the actuation pulse, u(k) [V], is designed such that the meniscus velocity, y(k) [m/sec], follows the desired trajectory, y d (k) [m/s], then the channel will come to rest very quickly after jetting the drop. This will reduce the interaction between the jetted drops at higher jetting frequencies. Several jetting bitmaps are tested, Figure 3.9 shows a sample of the tested bitmaps. This bitmap is transformed to a desired meniscus velocity with jetting frequency 50 khz as shown in Figure The preview time is chosen to include the whole jetting pattern. Figure 3.10 shows the response of the MIMO inverse feedforward control. It is clear that the residual oscillations have been highly damped using the feedforward input as shown in Figure Moreover, the effect of the crosstalk is not visible in the system response. The perfect tracking of the designed feedforward input leads to improvement of the damping of the channel, which brings the channel at rest after jetting the droplet and, therefore, ensures the same initial meniscus state for all the subsequent drops. Therefore this will result in consistent drop properties for all drops. The simulation results show that a considerable improvement in the printhead performance can be achieved by implementing the MIMO inverse controller compared with the performance of the standard pulse. Thus, the inverse input, shown in Figure 3.11, is applied to a real printhead and the results are compared with a standard pulse. The time history of the drops traveling from the nozzle plate to the paper are collected to analyze

50 3.6. MULTI-CHANNEL CONTROL 43 Figure 3.9: The bitmap to be printed. the performance of the printhead. Figure show the drop velocity of the jetted bitmap using the proposed MIMO inverse input and the standard pulse respectively. The performance is evaluated based on maximum drop velocity variation of the jetted drops. The maximum drop velocity variation is less than 1 m/sec for the inverse input while it is 2 m/sec for the standard pulse. The improvement in the drop velocity consistency achieved using the MIMO inverse has a great consequences on the print quality as depicted in Figures Figure 3.14 shows the printed bitmap, which has regular pattern when compared with Figure Using the feedforward input results in droplets with similar velocity and small position error of the dots. Only few drop are misplaced and merged together. On the other hand, the difference in the velocity of the drops printed by the standard pulse leads to large gap between the first two drops and the remaining drop. Moreover, many drops are merged together and form one large dot on the printing media.

51 44 MODEL-BASED FEEDFORWARD CONTROL FOR A DOD INKJET PRINTHEAD y y y 3 0 y y 5 0 y Time(µ sec) Time (µ sec) Figure 3.10: Reference meniscus velocity (dashed-line) and meniscus velocity using the proposed MIMO inverse feedforward input response (solid-line). u u u 3 20 u 4 20 u Time (µ sec) u Time(µ sec) Figure 3.11: The feedforward control inputs.

52 3.6. MULTI-CHANNEL CONTROL Drop speed (m/sec) 5 1 m/sec 4 3 N1 N2 N3 N4 N5 N Drop no. Figure 3.12: Optimal inversion: Drop velocity of the jetted bitmap for the 6 channels Drop speed (m/sec) m/sec N 1 N 2 N 3 N 4 N 5 N Drop no. Figure 3.13: Standard Pulse: Drop velocity of the jetted bitmap for the 6 channels.

53 46 MODEL-BASED FEEDFORWARD CONTROL FOR A DOD INKJET PRINTHEAD Figure 3.14: Printed bitmap using the proposed MIMO optimal inversion. Figure 3.15: Printed bitmap using the standard pulse.

54 3.7. CONCLUSIONS 47 Incomplete Unknown Input pulse Narrow gap model (G(s)) Meniscus speed Jetting & drop formation process Drop speed Drop size Figure 3.16: Schematic diagram of the inkjet printhead modeling. 3.7 Conclusions It has been demonstrated that feedforward control is a suitable control strategy to overcome the residual vibrations and the crosstalk. Consequently, the printing quality of the inkjet printhead is considerably improved, beyond current achievements. The experimental results have shown the validity of the inverse-based feedforward approach. Although the implementation of the inverse-based feedforward control leads to a considerable improvement of the printhead performance compared to the current performance, the required performance is not achieved yet, the drop-velocity variations are still higher than 1 m/s. As illustrated in Figure 3.16, the main reason is that the design of the input pulse is based on a model, which is incomplete. The narrow-gap model does not predict the meniscus position, which has a major effect on the drop velocity. Moreover, this model does not include the refill dynamics of ink inside the channel after jetting a drop. The jetting process and drop formation dynamics are not considered in the design of the input pulse.

55 48 MODEL-BASED FEEDFORWARD CONTROL FOR A DOD INKJET PRINTHEAD

56 49 Chapter 4 Experimental-Based Control for a DoD Inkjet Printhead In chapter 3, we have presented a model-based feedfoward control technique using the narrow-gap model. Although the implementation of the model-based technique has a considerable improvement of the printhead performance compared to the current performance, the desired performance is still not achieved yet. The printing quality is related to the drop velocity, which is affected by the meniscus state (both meniscus position and velocity) at firing instant. The state at the firing depends on the previous pixels in the bitmap (pixels on/off). The narrow-gap model does not include the dynamics of the meniscus position. The model of the jetting process and the drop formation is unknown. Consequently, with the available models, a proper input pulse cannot be designed. Moreover, there is no sensor available to measure the meniscus state and, therefore, we cannot identify a model based on measured data. The only available sensor is the CCD camera, which is used to monitor the jetted drops. Therefore, in this chapter, we develop a vision-based control strategy where the drop properties, i.e. velocity and volume, are measured using a CCD camera and the input pulse is optimized directly using the experimental setup. The input pulse is parameterized as function of the two resonance frequencies and the damping factor of the printhead. Moreover, we show that using this pulse structure, one can efficiently cope with single channel residual vibrations, crosstalk, and even generalize to optimization over arbitrary bitmaps that need to be printed.

57 50 EXPERIMENTAL-BASED CONTROL FOR A DOD INKJET PRINTHEAD 4.1 Introduction Recently, process performance optimization has received a great deal of attention, since it naturally allows for reducing production costs, improving product quality, and meeting safety requirements and environmental regulations. Optimization is typically based on a model that is used by a numerical algorithm to compute the optimal solution. In practice, however, an accurate model of the complex processes can hardly be identified or derived with affordable effort. The system identification is further complicated because the system measured data are usually noisy and signals often do not have sufficient information to allow for efficient system identification [29]. Therefore, optimization using an inaccurate model might result in suboptimal solutions or, even worse, infeasible solutions when constraints are present. Model uncertainty results primarily from trying to fit a model of limited complexity to a complex process system. Two main classes of optimization methods are available to handle these uncertainties. The first one is robust optimization, where it is assumed that the problem data is uncertain and it is only known to belong to some uncertainty set. The optimization is then performed by considering the worst case scenario [30]-[31]. However, this kind of methods requires the optimization of a highly complex model and that the optimal solution may become conservative. The second optimization method is the experimental-based optimization. Instead of initially building a model, the experimental-based optimization uses experimental measurements directly in conducting the optimization for the printing quality control. However, an experiment is different from a model prediction in the sense that it costs more time during the iterations. In this chapter, an experimental-based control strategy is developed to reduce the drop velocity variations due to the residual vibrations in case that a single channel is jetting. In [32], a new input pulse is presented, see Figure 4.1, which consists of two trapezoidal pulses, namely, a jetting pulse and a quenching pulse. The positive jetting pulse is used to form and jet the drop, however this pulse cannot damp the residual vibrations generated after jetting of the ink drop. Therefore, a negative quenching pulse is added to damp the residual vibrations.the optimal pulse parameters are obtained by solving an optimization problem, which minimizes the error between the actual drop velocity and a desired drop velocity. The drop properties depend on the bitmap to be printed. Therefore, based on the bitmap the input pulse is updated. The 0-pixel in the pattern will result in succeeding drops with different properties. The input pulse has to be updated based on the number of preceding 0-pixels in the pattern. Thus an optimization problem is formulated for several jetting patterns. This optimization problem results in a set of pulses, which reduces the drop velocity variations for any random bitmap.

58 4.1. INTRODUCTION 51 V A Input voltage for the piezo actuator T rf 1/2F 2 T rf 1/F 1 T rf Quenching pulse T rf 1/2F 2 Jetting pulse µ V A Time Figure 4.1: Parametrized input pulse. P 1 P 2 Figure 4.2: System response to the rising and falling edge of the input pulse.

59 52 EXPERIMENTAL-BASED CONTROL FOR A DOD INKJET PRINTHEAD 4.2 Input pulse parametrization Based on the physical effect of the input pulse parameters on the channel acoustics, the voltage pulse is parameterized as a function of two resonance frequencies and the damping factor of the printhead, see Figure 4.1. As explained in chapter 2, the jetting mechanism is related to the pressure wave of ink inside the channel. However, the pressure wave in ink generated by a waveform voltage is difficult to measure directly. In the setup, a self-sensing signal from a piezoelectric, the PAINT signal, can be used to measure the pressure wave behavior in a single nozzle printhead. However, this signal has a very low signal to noise ratio, which makes this signal little accurate. The motion of the meniscus at the nozzle plate results from a pressure wave of ink generated from piezoelectric actuation. The rising and falling times of the jetting pulse are used to generate the pressure wave inside the channel. The dwell time changes the relative phase of the generated pressure waves. At the rising edge, a negative pressure wave is generated, say P 1, while a positive pressure is generated at the falling edge, say P 2, see Figure 4.2. The rising and falling time of the jetting pulse is chosen to be the same to obtain the same characteristics of the pressure waves. To achieve the maximum pressure inside the channel and, therefore, the maximum drop velocity, the pressure waves, P 1 and P 2, have to be in phase. If the pressure waves generated from the rising and falling times have the same period with half period phase shift, an amplified pressure wave will be generated as a sum of the two pressure wavesp 1 and P 2. The period of the generated pressure waves is related to the jetting resonance frequency of the printhead, which is the second mode F 2 in the frequency response shown in Figure 3.3. Thus, the optimal dwell time of the pulse is chosen as half of the period of the second resonance frequencyf 2 as shown in Figure 4.1. The amplitude of the jetting pulse is designed to jet a droplet with specific properties: drop velocity and drop volume. For better printing performance, subsequent drops should not be jetted until the residual vibrations from the jetted drop have sufficiently damped out. These oscillations last for about 100 µsec, which limits the maximum jetting frequency to 10 khz. However, industrial applications require jetting at higher frequencies to achieve higher printing speed and/or higher print resolution. The quenching pulse is introduced to suppress the residual vibrations and, therefore, a higher jetting-frequency is obtained. To achieve perfect cancellation of the residual oscillations, the quenching pulse is chosen similar to the jetting pulse but with a negative sign. The optimal amplitude of the quenching pulse is equal to the amplitude of the resonating pulse multiplied by the damping factor µ of the printhead with opposite sign of the resonating pulse. The choice of the quenching time instant is very crucial. The quenching time should be chosen such that the

60 4.3. EXPERIMENTAL-BASED OPTIMIZATION 53 pressure wave generated by the jetting pulse is in anti-phase with the one generated by the quenching pulse. Therefore, the quenching pulse is placed at one period of the first resonance frequencyf 1. BothT rf andv A are chosen to achieve desired drop properties. If the exact values of the two frequency modes and the damping factor are known, the optimal pulse parameters to cope with the residual vibration can be easily obtained. To validate this new pulse parameterization and our assumptions, the narrow gap model is used to show that the residual vibration will be damped. We know that in this model F 1 = 78 khz, F 2 = 160 khz and the damping factor is µ = 0.5, by designing a pulse based on these parameters the residual vibration is highly damped as shown in Figure Experimental-based optimization In this section, we present an optimization-based approach to obtain the optimal parameters of the input pulse, see Figure 4.1. In this approach, the optimization is carried out on a real setup instead of using a printhead model. A schematic diagram of the approach is illustrated in Figure 4.4. We will be concerned with improving the drop properties, mainly the drop velocity. Therefore, we optimize the input pulse based on the drop velocity. In this approach, a high-speed camera is used to capture the drop, which is traveling from the nozzle plate to the printing media. A time history of the jetted drop is obtained. Using an image processing technique, the velocity of the jetted drops is estimated. The input pulse is optimized such that the error between the measured drop velocity v actual and a desired drop velocity v desired is minimized. The optimization process is done with a real printhead in the loop. No models are being used, hence all modeling issues are avoided. A schematic diagram of the approach is illustrated in Figure Image processing Image processing refers to the use of different computer algorithms to extract or modify specific information in (digital) images. The purpose is to transform the digital image into another digital image which is usually used for image coding, image enhancement, image restoration, and/or image feature extraction [34]- [35]. In our approach, image processing is used for feature extraction. The goal of image feature extraction technique is to transform the image into another image from which specific image features can be derived. Image based measurement has been widely applied in various kind of scientific applications as well as in many industrial and medical applications. The first scientific area that uses image processing is astronomy. In that area, the image processing techniques have

61 54 EXPERIMENTAL-BASED CONTROL FOR A DOD INKJET PRINTHEAD 6 5 Optimal pulse Standard pulse 4 Mensicus speed (m/sec) Time (µ sec) Figure 4.3: Simulation based on the narrow-gap mode. ` Optimized Pulse Parameters Optimization Algorithm Actual Drop Speed Image Processing Algorithm Image Desired Drop Speed Figure 4.4: Experimental-based optimization feedforward control approach.

62 4.3. EXPERIMENTAL-BASED OPTIMIZATION 55 been used to improve the quality of the pictures of the moon. Nowadays, vision feedback control has been introduced as a popular technique to increase the flexibility and the accuracy of robotic systems [36]. For example, the aim of the visual servo approach is to control a robot using the information provided by a vision system. It involves visual tasks, which are used in real time control of a production system, or in autonomous vehicle guidance such as navigation and collision avoidance. Moreover, image based measurement is very useful in situations when it is not possible to use human vision, such as underwater inspections, or in heavy polluted or hazardous environments such as nuclear power plants. In our approach, a high-speed camera is used to record the time history of the drops traveling from the nozzle plate to the printing media. An image processing technique is developed to retrieve the actual velocity of each drop. Two different samples of the time history of 5 drops are shown in Figure 4.5. These images illustrate the measured positions of drops with respect to the nozzle of the printhead as function of time. Both the jetted drops and small satellite drops are shown. The image processing algorithm extracts only informations of the jetted drops. Towards this objective, the image is converted into a binary image, which has only two possible values for each pixel. Typically the two colors used for a binary image are black and white, where a 0 is assigned for black and a 1 for white. After that, the image is filtered to remove the small dots that represent the satellites. The filter, used in our approach, creates a flat disk-shaped structuring element with a specific neighborhood. The neighborhood is defined as a matrix containing 1 s and 0 s; the location of the 1 s defines the neighborhood for the morphological operation. The center of the neighborhood is its center element. Based on the number of 1 s in the neighborhood, the image is filtered. Finally, a pattern recognition technique based on the 2D pixel search is developed to obtain the positions of each drop. Figure 4.5 shows examples of the time history of the five drops and the reconstructed image. Once the image is reconstructed, the velocity of each drop is computed based on linear fit of the drop position and the traveling time Optimization problem Experimental-based optimization adopts experimental measurements as function evaluations for optimization. Points are iteratively generated by a proper algorithm that provides the direction of improvement for the decision variables. An optimization algorithm, which reduces the number of test experiments, is desirable. As explained in section 4.2, the input pulse, see Figure 4.1, is parameterized with, θ := col(t rf,f 1, F 2, µ, V A ) R 5. with T rf [µs] denotes the rise and fall time, V A [V] is the jetting pulse amplitude,

63 56 EXPERIMENTAL-BASED CONTROL FOR A DOD INKJET PRINTHEAD Real Images 600 Reconstructed Images 500 Position Position (pixels) Time Time (pixels) Position Position (pixels) Time Time (pixels) Figure 4.5: Input and output of the image processing algorithm. F 1 [khz] and F 2 [khz] represent the first and the second resonance frequency of the printhead, respectively, andµ[-] is damping factor of the channel. The optimization problem is defined as subject to J(θ) = F max f=f min t=0 T (v desired (t,f) v actual (θ,t,f)) 2, (4.1) θ min θ θ max, (4.2) where f is the jetting frequency, which is the basic frequency of jetting a train of drops and it is sampled with sampling frequency0.5 khz,v desired (t,f) = 6m/s t, f is the desired drop velocity, v actual [m/s] is the actual drop velocity, T denotes the total time of the experiment, andtis the time instant when a measurement is taken with sampling time 5µs. θ min andθ max denote the lower and upper bounds of the decision variables, respectively, which are defined as θ min := col(0.5,65,150,0.25,12), θ max := col(2,85,170,0.75,40). The optimization is performed for jetting frequency range [F min,f max ]= [20, 60] khz.

64 4.3. EXPERIMENTAL-BASED OPTIMIZATION 57 The optimal pulse that minimizes the cost function is given by θ opt = arg min θ J(θ), (4.3) This problem formulation leads to a nonlinear optimization problem. A standard optimization algorithm is used to solve this constrained nonlinear optimization problem, which is not convex. The search algorithm can be generally categorized into two types, the gradient-based and gradient-free methods [37]-[39]. Gradient-based algorithms utilize gradients to provide search directions for improvement. The calculation of the gradient at a given point can be conducted by perturbations. Finite differencing is one method that is widely used for gradient calculations. Generally, gradient-based algorithms converge faster as the gradient leads to a good search direction for minimization. The gradient calculation based on the finite differences for the experimental-based optimization, however, needs a large number of experiments in case of a large number of decision variables. On the other hand, the gradient-free algorithm can be performed without computing the gradients, which in turn reduces the number of experiments required for the optimization. One of the standard gradient-free methods is based on Nelder-Mead simplex [40]. However, this technique is a heuristic search method that can converge to non-stationary points [41]. Therefore, we used a standard gradientbased algorithm to solve the optimization problem to minimize (4.1), namely, the trust region reflective algorithm [42]. This algorithm can efficiently handle the nonlinear constrained optimization problem. To avoid the algorithm getting trapped into a local minimum, the optimization problem is carried out several times using different initial values Experimental results In this section, the optimized pulse is applied to a real printhead and the results are compared with a standard pulse. Several tests are carried out to evaluate the efficiency of the optimized pulse. Figure 4.6 shows the DoD drop velocity curve for the optimized pulse and the standard pulse. The DoD curve is the velocity of the drop at several jetting frequencies when the nozzle is continuously jetting. The drop velocity variation for the optimized pulse is less than 1.4 m/s compared with variations of 6 m/s in case of the standard pulse over the jetting frequency range khz. We observe that the main contribution of the error is due to the low drop velocity at jetting frequencies between khz. The reason for the slow drop velocity at this frequency range could be that the two frequency modes, F 1 and F 2, and damping ratio µ of the printhead are different at this frequency range. Therefore, we focus on optimizing a second pulse only over this frequency range,f min = 20 khz andf max = 32kHz, and we obtained a new optimized pulse for this range, the optimized parameters are summarized in Table 4.1.

65 58 EXPERIMENTAL-BASED CONTROL FOR A DOD INKJET PRINTHEAD θ 1 (20-32 khz) θ 2 (32-70 khz) T rf F F µ V A Table 4.1: Optimized pulse parameters Now by defining two pulses, one for the low jetting frequency, khz, and another one for the rest of the jetting frequencies, the maximum drop velocity variation is less than 0.9 m/sec as shown in Figure 4.7. As depicted in Figure 4.8, the optimized pulse at the low-frequency range is not just a scaled version of the high-frequency optimized pulse. Note that the optimized pulses can be used for jetting drops with a DoD frequency up to jetting frequency 53 khz without overlapping of the pulse. The sudden change in the DoD speed curve at the jetting frequency53 khz is due to hardware limitations since the waveform generator cannot overlap the pulses. The second test is jetting a train of drops at several jetting frequencies and analyzing the time history of the drop traveling from the nozzle plate to the printing media. Figure 4.9 shows the time history of the train of drops for both the experimental-based optimized pulse and standard pulse, with a jetting frequency of 48 khz. The Figure compares the experimental results of using the optimized pulse (4.9-a) with the standard pulse (4.9-b). The application of the optimized pulse results in all the 16 drops traveling with the same velocity. The drops are disposed at an equal distance on the printing media. The first drop is, however, slower and therefore the drop is merged with the second drop. A small satellite drop is visible after the last drop. However, jetting with the standard pulse results in drops where the first drop travels to the printing media with high velocity, the subsequent drops travel with different velocities. Several drops are merged together into a single large drop. Consequently, the drops are misplaced on the printing media and have different sizes. Several experiments are carried out for various jetting frequencies ranging from 20 to 70 khz and the performance of the printhead is analyzed in terms of the drop velocity. The drop velocity of jetting10 drops over jetting frequencies20 70 khz is depicted in Figures , for the standard pulse and the vision-based feedforward optimized pulse, respectively. The vision-based feedforward pulse shows less drop velocity variation compared with the model-based feedforward input and standard pulse. The performance is evaluated based on the maximum drop velocity variation over the whole range of the DoD frequencies, the behavior of the first drop, and the maximum drop velocity variation at each DoD frequency. The maximum drop velocity variation

66 4.3. EXPERIMENTAL-BASED OPTIMIZATION Overlapping part 7 6 Drop velocity (m/s) Standard pulse (Max. deviation=6m/s) Optimized pulse (Max. deviation=1.4m/s) Jetting frequency (khz) Figure 4.6: DoD curve comparison of the standard and optimized pulses Drop velocity(m\sec) Overlapping part 2 1 One pulse Two pulses Jetting frequency (khz) Figure 4.7: Optimized DoD curve with two optimized pulses.

67 60 EXPERIMENTAL-BASED CONTROL FOR A DOD INKJET PRINTHEAD P 1 (20 32kHz) P 2 (32 70 khz) Amplitude (V) Time (µsec) Figure 4.8: Optimized pulses based on vision-based optimization. Paper location Distance Satellite drop Nozzle location Time (a) Optimized pulse Paper location Distance First drop Second drop The remaining drops are merged Nozzle location Time (b) Standard pulse Figure 4.9: Jetting16 drops at a DoD frequency48 khz.